Volumetric Caustics + HDRI Backdrop
You have to specify the exterior volume of the objects inside the fog cube.
Plug a pointer to the fog volume into the "exterior volume" slot of the two glass materials of the lenses and prism.

Note, the beam between lens on the right and prism still stays very weak. To be honest, I don't know what's up with that. It could be another problem in the volume setup or mesh normals, or it might be a bug in LuxCore.
You can try asking about it in our forum where our main LuxCore developer Dade might be able to tell you more about it.
In the forum I have also written a bit of an explanation about interior/exterior volume setup, maybe it helps you: https://forums.luxcorerender.org/viewtopic.php?f=4&amp;t=1178&amp;p=13864#p13879



Before:
(HDRI was not packed, so I used a green color instead)



After:



(30 second renders)

The prism

The last piece is the prism. Originally, I did my prism from the cube by eliminating one face and merging disconnected edges. Now I tried cleaner way by adding cylinder and setting number of faces to 3. This did the job. The two ways obviously don't lead to the same mesh.

Result:


Link to fixed scene is here and link to HDRI image here.